Solve 4y'' - 4y' + y = 0?

Question

solve this second order differential equation such that y(0)=0 and y(1)=1

Answer 1

4y"-4y'+y=??????????????????????????????...

Answer 2

4y'' - 4y' + y = 0

Find the characteristic equation:

4r^2 - 4r + 1 = 0

4r^2 - 2r - 2r + 1 = 0

2r(2r - 1) - (2r - 1) = 0

(2r - 1)(2r - 1) = 0, r = 1/2, r = 1/2

y = Ae^(t/2) + Bte^(t/2)

where A and B are the coefficients to be determined from the initial values.  

Answer 3

40-40+0=0 i guess thats right i am not good with math.